CN106354019A - Accurate control method for dissolved oxygen based on RBF neural network - Google Patents

Abstract

The invention relates to an accurate control method for dissolved oxygen based on an RBF neural network, belonging to the field of water treatment and the field of intelligent control. Aiming at the characteristics of high nonlinearity, high coupling property, time varying, large lag, serious uncertainty, and the like, of a sewage disposal process, the control method is characterized in that the processing capability of the neural network is improved by adjusting a neural network structure, and the control precision and stability are improved by establishing a prediction model based on the neural network and designing a neural network controller used for controlling; the problem of low adaptive ability of the present method based on switch control and PID control is solved; an experimental result proves that the method has higher dynamic response capability and self-adaptive capability, the accurate control on dissolved oxygen (DO) concentration can be realized and the sewage disposal effect can be improved and the energy consumption can be reduced.

Description

A kind of dissolved oxygen accuracy control method based on rbf neutral net

Technical field

The present invention is using based on rbf neural network sewage disposal system forecast model and design rbf neutral net control Device processed, realizes the control of dissolved oxygen do in sewage disposal process, and the control effect of dissolved oxygen do is directly connected to standard water discharge The problem whether situation and water factory's energy consumption can reduce.By the dissolved oxygen accuracy control method application based on rbf neutral net In sewage disposal system, precise control is carried out to dissolved oxygen do, you can to improve wastewater treatment efficiency, achieve in line traffic control again System, reduces energy consumption and operating cost simultaneously.The precise control of dissolved oxygen concentration belongs to water treatment field, belongs to intelligent control again Field processed.

Background technology

In recent years, China actively builds sewage treatment facility, the quick sewage treatment capacity promoting city and industrial scene. " China Environmental State Bulletin in 2015 " that Environment Protect in China portion issues is pointed out, in order to advance master；Want pollution reduction, increase newly 10,960,000 tons of town sewage daily handling ability, recycled water day 3,380,000 tons of Utilization ability, National urban wastewater treatment rate reaches 91.97%.And water body major pollutants are ammonia nitrogen, total phosphorus and chemical requirement.City produces sewage 91.97% all can be through dirt Water treatment plant is processed, to solve the problems, such as environmental pollution and shortage of water resources.But, due to the unconventional and unrestrained mark of Sewage Treatment Plant Rate is not high, and pollutant levels remove the major issue remaining in sewage disposal process such as inadequate, the especially place to industrial wastewater Reason.Therefore, the water of sewage treatment plant's discharge can cause certain pollution to soil and river.

At present, sewage treatment process, mainly with Aeration tank as core, by microbial degradation Organic substance, is realized to pollutant Removal.Keep dissolved oxygen in Aerobic Pond to maintain the concentration that growth of microorganism is suitable for, directly influence going of pollutant such as cod Except the degraded with other Organic substances, reduce water factory's processing cost while improving sewage disposal plant effluent compliance rate, therefore molten Solution oxygen concentration is the important control parameter of sewage treatment plant's processing procedure.

Controlling of dissolved oxygen is mainly adjusted by the valve opening adjusting aerator in aerating system.A part is dirty Water treatment plant is adjusted to aeration process using artificial experience, and its control effect is in close relations with human factorss, control can Cannot be guaranteed than relatively low and treatment effect by property.If blower air quantity is adjusted to the larger value that compares, to ensure Water water quality, then occur that situation is runed counter in energy waste and energy-saving and emission-reduction.Yet another part sewage treatment plant adopts pid to control System, in the case of keeping three link parameter constants of system, to the dirt with the features such as big time-varying, high non-linearity and close coupling Water treatment procedure, pid control cannot be realized effectively controlling.

In order to solve the problems, such as artificial experience and traditional pid control cannot solution it is proposed that molten based on neutral net The solution accurate On-line Control of oxygen.Artificial neural network has very strong self-learning capability, can be applied to dissolved oxygen controller Design.By build the hardware platforms such as data acquisition, data transfer and air compressor control achieve data acquisition with transmission with And the issuing and executing of control signal.Sewage disposal system mathematical model is set up based on data-driven, non-for sewage disposal The characteristic Design controllers such as linear and big time-varying.By the neural net model establishing of dissolved oxygen concentration and the integrated and embedded software of control In, develop intelligence control system.It is applied to controlling it is achieved that to dissolved oxygen concentration of sewage disposal process dissolved oxygen On-line Control, improves stability and the reliability of control, has ensured effluent quality simultaneously and has reduced with reducing consumption The operating cost that anthropic factor brings to interference and the operator of control process.

Content of the invention

Present invention obtains a kind of neutral net dissolved oxygen do concentration control method based on gradient descent algorithm, devise Rbf neural network prediction model and devise for control rbf nerve network controller solve sewage disposal process in Control problem；It is controlled by the method, in sewage, dissolved oxygen concentration can reach most preferably, solves in sewage disposal process Dissolved oxygen is difficult to the problem of precise control, improves the precision of dissolved oxygen do concentration control；Meanwhile, ensured sewage disposal process Stability and achieve On-line Control；

Present invention employs following technical scheme and realize step:

1. a kind of dissolved oxygen accuracy control method based on rbf neutral net,

It is controlled for dissolved oxygen do concentration in batch-type interval activated Sludge System, with aerator aeration rate for controlling Amount, dissolved oxygen do concentration is controlled volume；

It is characterized in that, comprise the following steps:

(1) the sewage disposal system forecast model based on rbf neutral net for the design, forecast model rbf neutral net is divided into Three layers: input layer, hidden layer and output layer；Forecast model rbf neutral net inputs as u (k)=[u₁(k),u₂(k)]^t, u₂(k) =u₁(k-1), u₁K () is k moment dissolved oxygen do concentration control amount, u₁(k-1) for the dissolved oxygen do concentration control amount in k-1 moment, t Transposition for matrix；Forecast model rbf neutral net is output as dissolved oxygen do concentration prediction value；Its calculation is as follows:

1. initialize forecast model rbf neutral net: determine the connected mode of neutral net 2-p-1, i.e. input layer nerve Unit is 2, and hidden layer neuron is p, and p is the positive integer more than 2；Output layer neuron is 1；Forecast model rbf nerve Network input layer to hidden layer connection weight be 1, hidden layer and output interlayer connection weight carry out in the range of [0,1] with Machine assignment；The output of neutral net is expressed as follows:

$y_m\left(k\right)=\underset{j=1}{\overset{p}{\σ}}{w}_j\left(k\right)f_j\left(u\right(k\left)\right)---\left(1\right)$

Wherein, y_mK () is the output of k moment forecast model rbf neutral net, w_j(k) be j-th neuron of hidden layer and The connection weight of output layer, j=1,2 ..., p；f_jIt is the output of forecast model rbf neutral net j-th neuron of hidden layer, Its computing formula is:

$f_j\left(u\right(k\left)\right)=\exp (-|\left|u\right(k)-{\mathrm{\μ}}_j(k\left)\right||/{\mathrm{\σ}}_j^2(k\left)\right)---\left(2\right)$

Wherein, μ_jK () represents j-th neuronal center value of k moment hidden layer, σ_jK () represents j-th god of k moment hidden layer Through first center width；

2. performance indications j of forecast model rbf neutral net are defined_m(k)

$j_m\left(k\right)=\frac{1}{2}{e}_m^2\left(k\right)---\left(3\right)$

e_m(k)=y (k)-y_m(k) (4)

Wherein, y (k) is the dissolved oxygen do concentration value of k moment actual measurement, e_mK () is k moment dissolved oxygen do concentration value Error；

3. the parameter of forecast model rbf neutral net is updated

${\mathrm{\δw}}_j\left(k\right)=\frac{\∂j_m\left(k\right)}{\∂w_j\left(k\right)}=-e_m\left(k\right)f_j\left(u\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(5\right)$

w_j(k+1)=w_j(k)-ηδw_j(k)=w_j(k)+ηe_m(k)f_j(u(k))(1-y(k))y(k)(6)

${\mathrm{\μ}}_j(k+1)={\mathrm{\μ}}_j\left(k\right)-\mathrm{\η}\frac{\∂j_m\left(k\right)}{\∂{\mathrm{\μ}}_j\left(k\right)}---\left(7\right)$

${\mathrm{\σ}}_j(k+1)={\mathrm{\σ}}_j\left(k\right)-\mathrm{\η}\frac{\∂j_m\left(k\right)}{\∂{\mathrm{\σ}}_j\left(k\right)}---\left(8\right)$

Wherein, δ w_jK () is the correction of j-th hidden layer neuron of k moment and output layer neuron connection weight, w_j K () is the connection weight of j-th hidden layer neuron of k moment and output layer neuron, w_j(k+1) it is to imply for j-th in the k+1 moment Layer neuron and the connection weight of output layer neuron, μ_j(k+1) j-th neuronal center value of k+1 moment hidden layer, σ are represented_j (k+1) represent the center width of k+1 j-th neuron of moment hidden layer；η is learning rate, η ∈ (0,1]；

4. judge the size of the object function of current time dissolved oxygen do prediction, if j_m(k) > 0.01, then repeat step ③；If j_mK () < 0.01, then go to the output y that 1. step calculates forecast model rbf neutral net_m(k)；

(2) it is designed for the rbf nerve network controller controlling；X (k)=[x₁(k),x₂(k)]^tFor rbf neutral net control The input of device processed, x₁K () is the error of k moment dissolved oxygen do concentration set point and actual value, x₂K () is that k moment dissolved oxygen do is dense Degree setting value and the rate of change of actual value error；

1. initialize rbf nerve network controller: determine the connected mode of neutral net 2-m-1, i.e. input layer For 2, hidden layer neuron is m, and m is the positive integer more than 2；Output layer neuron is 1；Rbf nerve network controller The connection weight of input layer to hidden layer is 1, and the connection weight of hidden layer and output interlayer is assigned in the range of [0,1] at random Value；The output of neutral net is expressed as follows:

$u\left(k\right)=\underset{i=1}{\overset{m}{\&sigma;}}{w}_i^c\left(k\right)f_i\left(x\right(k\left)\right)---\left(9\right)$

Wherein, u (k) is the output of k moment rbf nerve network controller, w_i ^cK () implies for rbf nerve network controller I-th neuron of layer and the connection weight of output layer, i=1,2 ..., m；f_iIt is rbf i-th neuron of neutral net hidden layer Output, its computing formula is:

$f_i\left(x\right(k\left)\right)=\exp (-|\left|x\right(k)-{\mathrm{\&mu;}}_i^c(k\left)\right||/{\left({\mathrm{\&sigma;}}_i^c\left(k\right)\right)}^2)---\left(10\right)$

Wherein, μ_i ^cK () represents k i-th neuronal center value of moment rbf nerve network controller hidden layer, σ_i ^c(k) table Show the center width of k i-th neuron of moment rbf nerve network controller hidden layer；

2. define index j of rbf nerve network controller_c(k)

$j_c\left(k\right)=\frac{1}{2}{e}^2\left(k\right)---\left(11\right)$

E (k)=r (k)-y (k) (12)

Wherein, e (k) is the error of k moment dissolved oxygen do concentration, and r (k) is k moment dissolved oxygen do concentration set point；

3. the parameter of rbf nerve network controller is updated

${\mathrm{\&delta;w}}_i^c\left(k\right)=\frac{\&part;j_c\left(k\right)}{\&part;w_i^c\left(k\right)}=-e\left(k\right)f\left(x\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(13\right)$

$w_i^c(k+1)=w_i^c\left(k\right)-{\mathrm{\&eta;}}_1{\mathrm{\&delta;w}}_i^c\left(k\right)=w_i^c\left(k\right)+{\mathrm{\&eta;}}_{1}e\left(k\right)f\left(x\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(14\right)$

${\mathrm{\&mu;}}_i^c(k+1)={\mathrm{\&mu;}}_i^c\left(k\right)-{\mathrm{\&eta;}}_1\frac{\&part;j_c\left(k\right)}{\&part;{\mathrm{\&mu;}}_i^c\left(k\right)}---\left(15\right)$

${\mathrm{\&sigma;}}_i^c(k+1)={\mathrm{\&sigma;}}_i^c\left(k\right)-{\mathrm{\&eta;}}_1\frac{\&part;j_c\left(k\right)}{\&part;{\mathrm{\&sigma;}}_i^c\left(k\right)}---\left(16\right)$

Wherein, δ w_i ^cK () is k i-th neuron of moment rbf nerve network controller hidden layer and output layer nerve Rhizoma Coptidis Meet the correction of weights, w_i ^c(k+1) rbf nerve network controller hidden layer the i-th neuron for the k+1 moment and output layer nerve The connection weight of unit；μ_i ^c(k+1) k+1 i-th neuronal center value of moment rbf nerve network controller hidden layer, σ are represented_i ^c(k + 1) represent the center width of k+1 i-th neuron of moment rbf nerve network controller hidden layer；η₁For learning rate, η₁∈(0, 1]；

4. judge the size of the object function of current time dissolved oxygen do, if j_c(k) > 0.01, then repeat step is 3.；As Fruit j_cK () < 0.01, then go to output u (k) that 1. step calculates rbf nerve network controller；

(3) using the u (k) solving, dissolved oxygen do is controlled, u (k) is controlled quentity controlled variable for the k moment for aeration rate, control System processed is output as the concentration value of actual dissolved oxygen do.

The creativeness of the present invention is mainly reflected in:

(1) present invention is a mistake with the features such as non-linear, close coupling, big time-varying for current sewage disposal process Journey, needs to control dissolved oxygen do concentration in a rational scope, but according to the existing control method of sewage treatment plant, difficult To realize stable and to be accurately controlled；Very strong self adaptation and self-learning capability are had according to neutral net, devises rbf nerve Network Prediction Model and rbf nerve network controller, it is achieved that the On-line Control of dissolved oxygen, have good stability, real-time is good And control accuracy high the features such as；

(2) present invention devises rbf neural network prediction model and rbf nerve network controller, and control method is preferably Solve the unmanageable problem of nonlinear system it is achieved that the real-time precise control of dissolved oxygen concentration；Solve the dirt of complexity Water treatment procedure only relies on solution artificial experience and realizes control problem, has the features such as energy consumption is low, and structure is simple；

Brief description

Fig. 1 is neural net model establishing of the present invention and controller architecture figure

Fig. 2 is rbf neutral net network structure of the present invention

Fig. 3 is control system dissolved oxygen do concentration results figure of the present invention

Fig. 4 is control system dissolved oxygen do concentration error figure of the present invention

Specific embodiment

Present invention obtains a kind of neutral net dissolved oxygen do concentration control method based on gradient descent algorithm it is achieved that The precise control of dissolved oxygen do concentration in sewage disposal process；The method is the method by being declined based on data-driven and gradient Solve the control problem in sewage disposal process；After being controlled by the method, in sewage, dissolved oxygen concentration can reach Good, solve the problems, such as that in sewage disposal process, dissolved oxygen is difficult to precise control, improve the precision of dissolved oxygen do concentration control； Meanwhile, ensure the stability of sewage disposal process and achieve On-line Control；

Present invention employs following technical scheme and realize step:

A kind of dissolved oxygen accuracy control method based on rbf neutral net,

It is controlled for dissolved oxygen do concentration in batch-type interval activated Sludge System, with aerator aeration rate for controlling Amount, dissolved oxygen do concentration is controlled volume, control structure figure such as Fig. 1；

(1) the sewage disposal system forecast model based on rbf neutral net for the design, forecast model rbf neutral net is divided into Three layers: input layer, hidden layer and output layer；Prediction mould rbf neutral net inputs as u (k)=[u₁(k),u₂(k)]^t, u₂(k)= u₁(k-1), u₁K () is k moment dissolved oxygen do concentration control amount, u₁(k-1) for the dissolved oxygen do concentration control amount in k-1 moment, t is The transposition of matrix；Forecast model rbf neutral net is output as dissolved oxygen do concentration prediction value；Its calculation is as follows:

1. initialize forecast model rbf neutral net: determine the connected mode of neutral net 2-p-1, i.e. input layer nerve Unit is 2, and hidden layer neuron is 15 for p；Output layer neuron is 1；Forecast model rbf neural network input layer is to hidden Connection weight containing layer is 1, and the connection weight of hidden layer and output interlayer carries out random assignment in the range of [0,1]；Nerve net The output of network is expressed as follows:

$y_m\left(k\right)=\underset{j=1}{\overset{p}{\&sigma;}}{w}_j\left(k\right)f_j\left(u\right(k\left)\right)---\left(17\right)$

Wherein, y_mK () is the output of k moment forecast model rbf neutral net, w_j(k) be j-th neuron of hidden layer and The connection weight of output layer, j=1,2 ..., p；f_jIt is the output of forecast model rbf neutral net j-th neuron of hidden layer, Its computing formula is:

$f_j\left(u\right(k\left)\right)=\exp (-|\left|u\right(k)-{\mathrm{\&mu;}}_j(k\left)\right||/{\mathrm{\&sigma;}}_j^2(k\left)\right)---\left(18\right)$

Wherein, μ_jK () represents j-th neuronal center value of k moment hidden layer, σ_jK () represents j-th god of k moment hidden layer Through first center width；

2. performance indications j of forecast model rbf neutral net are defined_m(k)

$j_m\left(k\right)=\frac{1}{2}{e}_m^2\left(k\right)---\left(19\right)$

e_m(k)=y (k)-y_m(k) (20)

Wherein, y (k) is the dissolved oxygen do concentration value of k moment actual measurement, e_mK () is k moment dissolved oxygen do concentration value Error；

3. the parameter of forecast model rbf neutral net is updated

${\mathrm{\&delta;w}}_j\left(k\right)=\frac{\&part;j_m\left(k\right)}{\&part;w_j\left(k\right)}=-e_m\left(k\right)f_j\left(u\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(21\right)$

w_j(k+1)=w_j(k)-ηδw_j(k)=w_j(k)+ηe_m(k)f_j(u(k))(1-y(k))y(k) (22)

${\mathrm{\&mu;}}_j(k+1)={\mathrm{\&mu;}}_j\left(k\right)-\mathrm{\&eta;}\frac{\&part;j_m\left(k\right)}{\&part;{\mathrm{\&mu;}}_j\left(k\right)}---\left(23\right)$

${\mathrm{\&sigma;}}_j(k+1)={\mathrm{\&sigma;}}_j\left(k\right)-\mathrm{\&eta;}\frac{\&part;j_m\left(k\right)}{\&part;{\mathrm{\&sigma;}}_j\left(k\right)}---\left(24\right)$

Wherein, δ w_jK () is the correction of j-th hidden layer neuron of k moment and output layer neuron connection weight, w_j K () is the connection weight of j-th hidden layer neuron of k moment and output layer neuron, w_j(k+1) it is to imply for j-th in the k+1 moment Layer neuron and the connection weight of output layer neuron, μ_j(k+1) j-th neuronal center value of k+1 moment hidden layer, σ are represented_j (k+1) represent the center width of k+1 j-th neuron of moment hidden layer；Learning rate η=0.1；

4. judge the size of the object function of current time dissolved oxygen do prediction, if j_m(k) > 0.01, then repeat step ③；If j_mK () < 0.01, then go to the output y that 1. step calculates forecast model rbf neutral net_m(k)；

(2) it is designed for the rbf nerve network controller controlling；X (k)=[x₁(k),x₂(k)]^tFor rbf neutral net control The input of device processed, x₁K () is the error of k moment dissolved oxygen do concentration set point and actual value, x₂K () is that k moment dissolved oxygen do is dense Degree setting value and the rate of change of actual value error；

1. initialize rbf nerve network controller: determine the connected mode of neutral net 2-m-1, i.e. input layer For 2, hidden layer neuron is 17 for m；Output layer neuron is 1；Rbf nerve network controller input layer is to hidden layer Connection weight be 1, hidden layer and output interlayer connection weight carry out random assignment in the range of [0,1]；Neutral net Output is expressed as follows:

$u\left(k\right)=\underset{i=1}{\overset{m}{\&sigma;}}{w}_i^c\left(k\right)f_i\left(x\right(k\left)\right)---\left(25\right)$

Wherein, u (k) is the output of k moment rbf nerve network controller, w_i ^cK () implies for rbf nerve network controller I-th neuron of layer and the connection weight of output layer, i=1,2 ..., m；f_iIt is rbf i-th neuron of neutral net hidden layer Output, its computing formula is:

$f_i\left(x\right(k\left)\right)=\exp (-|\left|x\right(k)-{\mathrm{\&mu;}}_i^c(k\left)\right||/{\left({\mathrm{\&sigma;}}_i^c\left(k\right)\right)}^2)---\left(26\right)$

Wherein, μ_i ^cK () represents k i-th neuronal center value of moment rbf nerve network controller hidden layer, σ_i ^c(k) table Show the center width of k i-th neuron of moment rbf nerve network controller hidden layer；

2. define index j of rbf nerve network controller_c(k)

$j_c\left(k\right)=\frac{1}{2}{e}^2\left(k\right)---\left(27\right)$

E (k)=r (k)-y (k) (28)

Wherein, e (k) is the error of k moment dissolved oxygen do concentration, and r (k) is k moment dissolved oxygen do concentration set point；

3. the parameter of rbf nerve network controller is updated

${\mathrm{\&delta;w}}_i^c\left(k\right)=\frac{\&part;j_c\left(k\right)}{\&part;w_i^c\left(k\right)}=-e\left(k\right)f\left(x\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(29\right)$

$w_i^c(k+1)=w_i^c\left(k\right)-{\mathrm{\&eta;}}_1{\mathrm{\&delta;w}}_i^c\left(k\right)=w_i^c\left(k\right)+{\mathrm{\&eta;}}_{1}e\left(k\right)f\left(x\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(30\right)$

${\mathrm{\&mu;}}_i^c(k+1)={\mathrm{\&mu;}}_i^c\left(k\right)-{\mathrm{\&eta;}}_1\frac{\&part;j_c\left(k\right)}{\&part;{\mathrm{\&mu;}}_i^c\left(k\right)}---\left(31\right)$

${\mathrm{\&sigma;}}_i^c(k+1)={\mathrm{\&sigma;}}_i^c\left(k\right)-{\mathrm{\&eta;}}_1\frac{\&part;j_c\left(k\right)}{\&part;{\mathrm{\&sigma;}}_i^c\left(k\right)}---\left(32\right)$

Wherein, δ w_i ^cK () is k i-th neuron of moment rbf nerve network controller hidden layer and output layer nerve Rhizoma Coptidis Meet the correction of weights, w_i ^c(k+1) rbf nerve network controller hidden layer the i-th neuron for the k+1 moment and output layer nerve The connection weight of unit；μ_i ^c(k+1) k+1 i-th neuronal center value of moment rbf nerve network controller hidden layer, σ are represented_i ^c(k + 1) represent the center width of k+1 i-th neuron of moment rbf nerve network controller hidden layer；Learning rate, η₁=0.1；

4. judge the size of the object function of current time dissolved oxygen do, if j_c(k) > 0.01, then repeat step is 3.；As Fruit j_cK () < 0.01, then go to output u (k) that 1. step calculates rbf nerve network controller；

(3) using the u (k) solving, dissolved oxygen do is controlled, u (k) is controlled quentity controlled variable for the k moment for aeration rate, control System processed is output as the concentration value of actual dissolved oxygen do；The dissolved oxygen do concentration value of Fig. 3 display system, x-axis: time, unit It is 15 minutes/sample, y-axis: dissolved oxygen do concentration, unit is mg/litre, and solid line is expectation dissolved oxygen do concentration value, and dotted line is Actual dissolved oxygen do exports concentration value；Reality output dissolved oxygen do concentration and the error such as Fig. 4 expecting dissolved oxygen do concentration, x-axis: Time, unit is 15 minutes/sample, y-axis: dissolved oxygen do concentration error value, unit is mg/litre, and result proves the method Effectiveness.

Claims (1)

1. a kind of dissolved oxygen accuracy control method based on rbf neutral net,

It is controlled for dissolved oxygen do concentration in batch-type interval activated Sludge System, with aerator aeration rate as controlled quentity controlled variable, Dissolved oxygen do concentration is controlled volume；

It is characterized in that, comprise the following steps:

(1) the sewage disposal system forecast model based on rbf neutral net for the design, forecast model rbf neutral net is divided into three layers: Input layer, hidden layer and output layer；Forecast model rbf neutral net inputs as u (k)=[u₁(k),u₂(k)]^t, u₂(k)=u₁ (k-1), u₁K () is k moment dissolved oxygen do concentration control amount, u₁(k-1) for the dissolved oxygen do concentration control amount in k-1 moment, t is square The transposition of battle array；Forecast model rbf neutral net is output as dissolved oxygen do concentration prediction value；Its calculation is as follows:

1. initialize forecast model rbf neutral net: determine the connected mode of neutral net 2-p-1, that is, input layer is 2 Individual, hidden layer neuron is p, and p is the positive integer more than 2；Output layer neuron is 1；Forecast model rbf neutral net is defeated The connection weight entering layer to hidden layer is 1, and the connection weight of hidden layer and output interlayer is assigned in the range of [0,1] at random Value；The output of neutral net is expressed as follows:

$y_m\left(k\right)=\underset{j=1}{\overset{p}{\&sigma;}}{w}_j\left(k\right)f_j\left(u\right(k\left)\right)---\left(1\right)$

Wherein, y_mK () is the output of k moment forecast model rbf neutral net, w_jK () is j-th neuron of hidden layer and output The connection weight of layer, j=1,2 ..., p；f_jIt is the output of forecast model rbf neutral net j-th neuron of hidden layer, its meter Calculating formula is:

$f_j\left(u\right(k\left)\right)=\exp (-|\left|u\right(k)-{\mathrm{\&mu;}}_j(k\left)\right||/{\mathrm{\&sigma;}}_j^2(k\left)\right)---\left(2\right)$

Wherein, μ_jK () represents j-th neuronal center value of k moment hidden layer, σ_jK () represents k j-th neuron of moment hidden layer Center width；

2. performance indications j of forecast model rbf neutral net are defined_m(k)

$j_m\left(k\right)=\frac{1}{2}{e}_m^2\left(k\right)---\left(3\right)$

e_m(k)=y (k)-y_m(k) (4)

Wherein, y (k) is the dissolved oxygen do concentration value of k moment actual measurement, e_mK () is the error of k moment dissolved oxygen do concentration value；

3. the parameter of forecast model rbf neutral net is updated

${\mathrm{\&delta;w}}_j\left(k\right)=\frac{\&part;j_m\left(k\right)}{\&part;w_j\left(k\right)}=-e_m\left(k\right)f_j\left(u\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(5\right)$

w_j(k+1)=w_j(k)-ηδw_j(k)=w_j(k)+ηe_m(k)f_j(u(k))(1-y(k))y(k) (6)

${\mathrm{\&mu;}}_j(k+1)={\mathrm{\&mu;}}_j\left(k\right)-\mathrm{\&eta;}\frac{\&part;j_m\left(k\right)}{\&part;{\mathrm{\&mu;}}_j\left(k\right)}---\left(7\right)$

${\mathrm{\&sigma;}}_j\left(k+1\right)={\mathrm{\&sigma;}}_j\left(k\right)-\mathrm{\&eta;}\frac{\&part;j_m\left(k\right)}{\&part;{\mathrm{\&sigma;}}_j\left(k\right)}---\left(8\right)$

Wherein, δ w_jK () is the correction of j-th hidden layer neuron of k moment and output layer neuron connection weight, w_jK () is J-th hidden layer neuron of k moment and the connection weight of output layer neuron, w_j(k+1) it is j-th hidden layer god of k+1 moment Connection weight through unit and output layer neuron, μ_j(k+1) j-th neuronal center value of k+1 moment hidden layer, σ are represented_j(k+1) Represent the center width of k+1 j-th neuron of moment hidden layer；η is learning rate, η ∈ (0,1]；

4. judge the size of the object function of current time dissolved oxygen do prediction, if j_m(k) > 0.01, then repeat step is 3.；As Fruit j_mK () < 0.01, then go to the output y that 1. step calculates forecast model rbf neutral net_m(k)；

(2) it is designed for the rbf nerve network controller controlling；X (k)=[x₁(k),x₂(k)]^tFor rbf nerve network controller Input, x₁K () is the error of k moment dissolved oxygen do concentration set point and actual value, x₂K () sets for k moment dissolved oxygen do concentration Definite value and the rate of change of actual value error；

1. initialize rbf nerve network controller: determine the connected mode of neutral net 2-m-1, that is, input layer is 2 Individual, hidden layer neuron is m, and m is the positive integer more than 2；Output layer neuron is 1；Rbf nerve network controller inputs The connection weight of layer to hidden layer is 1, and the connection weight of hidden layer and output interlayer carries out random assignment in the range of [0,1]； The output of neutral net is expressed as follows:

$u\left(k\right)=\underset{i=1}{\overset{m}{\&sigma;}}{w}_i^c\left(k\right)f_i\left(x\right(k\left)\right)---\left(9\right)$

Wherein, u (k) is the output of k moment rbf nerve network controller, w_i ^cK () is rbf nerve network controller hidden layer i-th Individual neuron and the connection weight of output layer, i=1,2 ..., m；f_iIt is the defeated of rbf neutral net i-th neuron of hidden layer Go out, its computing formula is:

$f_i\left(x\right(k\left)\right)=\exp (-|\left|x\right(k)-{\mathrm{\&mu;}}_i^c(k\left)\right||/{\left({\mathrm{\&sigma;}}_i^c\left(k\right)\right)}^2)---\left(10\right)$

Wherein, μ_i ^cK () represents k i-th neuronal center value of moment rbf nerve network controller hidden layer, σ_i ^cWhen () represents k k Carve the center width of rbf nerve network controller i-th neuron of hidden layer；

2. define index j of rbf nerve network controller_c(k)

$j_c\left(k\right)=\frac{1}{2}{e}^2\left(k\right)---\left(11\right)$

E (k)=r (k)-y (k) (12)

Wherein, e (k) is the error of k moment dissolved oxygen do concentration, and r (k) is k moment dissolved oxygen do concentration set point；

3. the parameter of rbf nerve network controller is updated

${\mathrm{\&delta;w}}_i^c\left(k\right)=\frac{\&part;j_c\left(k\right)}{\&part;w_i^c\left(k\right)}=-e\left(k\right)f\left(x\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(13\right)$

$w_i^c(k+1)=w_i^c\left(k\right)-{\mathrm{\&eta;}}_1{\mathrm{\&delta;w}}_i^c\left(k\right)=w_i^c\left(k\right)+{\mathrm{\&eta;}}_{1}e\left(k\right)f\left(x\right(k\left)\right)(1-y(k\left)\right)y\left(k\right)---\left(14\right)$

${\mathrm{\&mu;}}_i^c(k+1)={\mathrm{\&mu;}}_i^c\left(k\right)-{\mathrm{\&eta;}}_1\frac{\&part;j_c\left(k\right)}{\&part;{\mathrm{\&mu;}}_i^c\left(k\right)}---\left(15\right)$

${\mathrm{\&sigma;}}_i^c(k+1)={\mathrm{\&sigma;}}_i^c\left(k\right)-{\mathrm{\&eta;}}_1\frac{\&part;j_c\left(k\right)}{\&part;{\mathrm{\&sigma;}}_i^c\left(k\right)}---\left(16\right)$

Wherein, δ w_i ^cK () is k i-th neuron of moment rbf nerve network controller hidden layer and output layer neuron connection weight The correction of value, w_i ^c(k+1) rbf nerve network controller hidden layer the i-th neuron for the k+1 moment and output layer neuron Connection weight；μ_i ^c(k+1) k+1 i-th neuronal center value of moment rbf nerve network controller hidden layer, σ are represented_i ^c(k+1) Represent the center width of k+1 i-th neuron of moment rbf nerve network controller hidden layer；η₁For learning rate, η₁∈(0,1]；

4. judge the size of the object function of current time dissolved oxygen do, if j_c(k) > 0.01, then repeat step is 3.；If j_c K () < 0.01, then go to output u (k) that 1. step calculates rbf nerve network controller；

(3) using the u (k) solving, dissolved oxygen do is controlled, u (k) is controlled quentity controlled variable for the k moment for aeration rate, controls system System is output as the concentration value of actual dissolved oxygen do.